On external fields created by fixed charges

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:464

Article

Orive, R.¹  Sanchez Lara, J. F.² 

[1] Univ La Laguna, Dept Anal Matemat, Canary Isl, Spain

[2] Univ Granada, Dept Matemat Aplicada, Granada, Spain

关键词: Equilibrium measures;    External fields;    Phase transitions;   

DOI  :  10.1016/j.jmaa.2018.03.078

来源: Elsevier

【 摘 要 】

In this paper equilibrium measures in the presence of external fields created by fixed charges are analyzed. These external fields are a particular case of the so-called rational external fields (in the sense that their derivatives are rational functions). Along with some general results, a thorough analysis of the particular case of two fixed negative charges (attractors) is presented; indeed, the main result of the paper deals with this particular case. As for the main tools used, this paper is a natural continuation of [31], where polynomial external fields were thoroughly studied, and [37], where rational external fields with a polynomial part were considered. However, the absence of the polynomial part in the external fields analyzed in the current paper adds a considerable difficulty to solve the problem and justifies its separated treatment; moreover, it is noteworthy to point out the simplicity and beauty of the results obtained. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free